I think it just matter of the preference and convenience for each person. I do it all the time , i age the water for 24 hrs only because i just learned this way from some one and it just convenient for me to match the water temperature so i don't have to acclimate my bettas like everyone else. I just put the changing cup in the new water and let them slowly to swim out. I did had accident long time ago when i didn't realized about temperature difference. I change the betta and the difference was like 8* and he was kind of lethargic for a few hrs. So i got paranoid about temp and just let water sit out . And btw it very convenient for small tanks and during the summer when you don't really need the heaters.

My fiance thinks it's easier to have aged and conditioned water ready to go in the jugs, so we'll probably stick with that method. The only downside is that the aged water tends to be a couple of degrees cooler than the water in Rakki's bowl. I'm not sure why that is, but I've been setting the jug we'll be using in a sink filled with warmer water to bring it up to the temperature we need.

I would think my water also probobly a few degree off but i never had any problem. What i do i just hold my guy in the cup and slowly add a little bit water a few times , then i let water out a little bit and add more new water,and then i let him swim out very slowly. I just put the cup sideways and hold it until he swims out of it. I also always rinse my hands (without soap)before i do anything with my bettas.

You also can have him in the changing cup with about 15% of the water and keep adding small amount of the water every 3-4 min for about 4 times.Make sure you cover the container he is in so he don't jump out.

In the winter time when i have heaters i do that:
When I change the water I put him in the cup I got him in then I take everything out of the tank, rinse everything with warm tap water. Then I put everything back in the tank, fill it with dechlorinated new water, and then turn the heater on. When the tank water is the same as the cup water , then take the dirty cup water out and a little at a time and put clean tank water in the cup. After that I put the cup in the tank and he swims out.

aging water has one benefit, it will help remove 'bubbles' in the water. sometimes you notice lots of bubbles in the tank or on your fish after a major water change. apparently some fish can develop sbd from the bubbles so people age it for a couple hours to help the extra gas evaporate.

I personally don't do it, I just condition and use a thermometer to make sure its the right temp. but nothing wrong if you no age your water! just make sure you are using conditioner.

The aging of water is an old, traditional method of water preparation. Before there were good, effective dechlorinators, aging allowed the chlorine in the tapwater to evaporate (outgas, actually). Nowadays, when water supplies typically contain chloramine, aging is useless for this purpose. A dechlorinater/conditioner must be used. These conditioners work instantaneously; so their is no practical reason to age water in this day and age.

As for temperature-matching. Use a thermometer for a while; eventually you'll learn to judge temperature by touch. This is close enough. If your refill water is a few degrees cooler than the tank water, it will be as though a rainfall has cooled the paddy or pool. Your fish will likely start looking around for a mate.

My water changes pH significantly from straight from the tap to a 24 airing out/aging. Using the API freshwater master test kit for pH and High range pH. This is why I will continue to use aged water even though I use a water conditioner.